Closed-loop (feedback) control is commonly employed in control systems. The frequency response of the closed-loop control system can be characterized by the presence of “poles” and “zeros”, which are derived from the transfer function that describes that system. The closed-loop control system may be represented graphically by plotting the locations of the poles and zeros on the complex s-plane. The frequency response may be represented graphically in terms of its gain and phase components as a function of frequency. Poles cause a decrease in gain magnitude and phase lag of 90 degrees with frequency, whereas zeros cause an increase in gain magnitude and a phase lead of 90 degrees with frequency.
Often a compensation network is added to the feedback loop or path of the closed-loop control system to obtain stability. Precise locations of the poles and zeros depend on both the desired characteristics of the closed-loop frequency response and the characteristics of the system being controlled.
A lead-lag compensator is a type of compensation network that improves an undesirable system stability and transient response in the system. The lead portion of the lead-lag compensator provides phase lead at high frequencies, which shifts poles to the left for increased damping and phase margin (and therefore increased stability). The lag portion of the lead-lag compensator provides phase lag at low frequencies and a dominant pole.